## Chaotic communication in radio-over-fiber transmission based on optoelectronic feedback semiconductor lasers

Optics Express, Vol. 15, Issue 2, pp. 302-311 (2007)

http://dx.doi.org/10.1364/OE.15.000302

Acrobat PDF (327 KB)

### Abstract

Performance of chaotic communication in radio-over-fiber (ROF) transmission based on optoelectronic feedback semiconductor lasers is studied numerically. The chaotic carrier is generated by optoelectronic feedback semiconductor lasers, where chaotic communication is realized by synchronizing a receiver laser with a transmitter laser. Transmission quality of different message encoding schemes, including additive chaos modulation (ACM) and on-off shift keying (OOSK), are investigated and compared. In this study, the dispersion and nonlinearity effects in the fiber transmission module and the amplified spontaneous emission noise from the optical amplifiers are considered. In the wireless channel, effects of additive white Gaussian noise, multipath, and path loss are included. To quantitatively study the performance of this chaotic communication system in the ROF transmission, bit-error-rates (BER) of different transmission lengths, message bit-rates, and signal-to-noise ratios are studied. The optimal launched power and message strength that minimize the BER while assuring effective communication security are discussed. While the ACM scheme is shown to perform better in a fiber only configuration, the OOSK scheme shows better immunity to the random effects and waveform distortions presented in the wireless channel.

© 2007 Optical Society of America

## 1. Introduction

1. F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. **221**,173–180 (2003). [CrossRef]

3. T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling route to chaos in a semiconductor laser subject to optical injection,” Appl. Phys. Lett. **64**,3539–3541 (1994). [CrossRef]

4. T. Mukai and K. Otsuka, “New route to optical chaos: successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. **55**,1711–1714 (1985). [CrossRef] [PubMed]

5. J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. **28**,93–108 (1992). [CrossRef]

6. F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. **39**,562–568 (2003). [CrossRef]

7. S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. **37**,329–336 (2001). [CrossRef]

8. F. Y. Lin and J. M. Liu, “Harmonic frequency locking in a semiconductor laser with delayed negative optoelectronic feedback,” Appl. Phys. Lett. **81**,3128–3120 (2002). [CrossRef]

9. N. Gastaud, S. Poinsot, L. Larger, J. M. Merolla, M. Hanna, J. P. Goedgebuer, and F. Malassenet, ”Electro-optical chaos for multi-10 Gbit/s optical transmissions” Electron. Lett. **40**, (2004). [CrossRef]

10. J. M. Liu, H. F. Chen, and S. Tang, ”Synchronized chaotic optical communications at high bit rates,” IEEE J. Quantum Electron. **38**,1184–1196 (2002). [CrossRef]

10. J. M. Liu, H. F. Chen, and S. Tang, ”Synchronized chaotic optical communications at high bit rates,” IEEE J. Quantum Electron. **38**,1184–1196 (2002). [CrossRef]

11. J. Ohtsubo, ”Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. **38**,1141–1154 (2002). [CrossRef]

12. Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, ”Communication using synchronization of optical-feedback-induced chaos in semiconductor lasers,” IEEE Trans. Circuits Syst. I **48**,1484–1490 (2001). [CrossRef]

13. D. Kanakidis, A. Argyris, and D. Syvridis, ”Performance characterization of high-bit-rate optical chaotic communication systems in a back-to-back configuration,” J. of Lightwave Technol. **21**,750–758 (2003). [CrossRef]

14. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, ”Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature **438**,343–346 (2005). [CrossRef] [PubMed]

15. D. Kanakidis, A. Bogris, A. Argyris, and D. Syvridis, ”Numerical investigation of fiber transmission of a chaotic encrypted message using dispersion compensation schemes,” J. of Lightwave Technol. **22**,2256–2263 (2004). [CrossRef]

## 2. Simulation model

### 2.1. Transmitter and receiver lasers

16. S. Tang and J. M. Liu, ”Chaos synchronization in semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. **39**,708–715 (2003). [CrossRef]

17. H. D. I. Abarbanel, M. B. Kennel, L. Illing, S. Tang, H. F. Chen, and J. M. Liu, ”Synchronization and communication using semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. **37**,1301–1311 (2001). [CrossRef]

1. F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. **221**,173–180 (2003). [CrossRef]

6. F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. **39**,562–568 (2003). [CrossRef]

*a*is the normalized field, ϕ is the optical phase,

*ñ*is the normalized carrier density,

*γ*,

_{c}*γ*,

_{s}*γ*, and

_{n}*γ*are the cavity decay rate, spontaneous carrier decay rate, differential carrier relaxation rate and the nonlinear carrier relaxation rate, respectively,

_{p}*b*is the linewidth enhancement factor, and

*J*̃ is the normalized dimensionless injection current parameter. The subscript

*r*and

*t*refer to the transmitter and the receiver lasers respectively. For the transmitter laser, the output is fed back with a feedback strength ξ

_{t}and a delay time τ

_{t}, while the receiver laser is injected with a coupling strength ξ

_{r}and a transmission propagation time τ

_{r}, respectively. In our simulation, the following experimentally measured intrinsic dynamical parameters of a high-speed semiconductor laser [18

18. J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron. **30**,957–965 (1994). [CrossRef]

*γ*= 2.4 × 10

_{c}^{11}

*s*

^{-1},

*γ*= 1.458 × 10

_{s}^{9}

*s*

^{-1},

*γ*= 3

_{n}*J*̃ × 10

^{9}

*s*

^{-1},

*γ*= 3.6

_{p}*J*̃ × 10

^{9}

*s*

^{-1}, and

*b*= 4. The lasers are both biased at a value of

*J*̃ = 1/3, while the feedback and coupling strengths ξ

*and ξ*

_{t}_{r}are both set to a level of 0.1. With this coupling strength, the receiver laser is operated in a linear operation regime that it is identically synchronized to the transmitter laser [16

16. S. Tang and J. M. Liu, ”Chaos synchronization in semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. **39**,708–715 (2003). [CrossRef]

17. H. D. I. Abarbanel, M. B. Kennel, L. Illing, S. Tang, H. F. Chen, and J. M. Liu, ”Synchronization and communication using semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. **37**,1301–1311 (2001). [CrossRef]

*f*= (

_{r}*γ*

_{c}*γ*+

_{n}*γ*

_{s}*γ*)

_{p}^{1/2}/2

*π*, which is about 2.49 GHz with the parameters used in this simulation. Second-order Runge-Kutta method is used to solve these coupled rate equations.

### 2.2. ACM and OOSK message encoding schemes

## 3. Fiber transmission module

### 3.1. Description of the fiber transmission module

15. D. Kanakidis, A. Bogris, A. Argyris, and D. Syvridis, ”Numerical investigation of fiber transmission of a chaotic encrypted message using dispersion compensation schemes,” J. of Lightwave Technol. **22**,2256–2263 (2004). [CrossRef]

*A*is the complex intracavity laser field amplitude,

*z*is the propagation distance,

*T*is the time measured in a reference frame moving at group velocity, α is the fiber attenuation coefficient, γ is the nonlinear coefficient, and β

_{2}and β

_{3}are the second-order and third-order chromatic dispersions. The split-step Fourier method (SSFM) [19

19. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, ”Optimization of the split-step Fourier method in modeling optical-fiber communication systems,” J. Lightwave Technol. **21**,61–68 (2003). [CrossRef]

15. D. Kanakidis, A. Bogris, A. Argyris, and D. Syvridis, ”Numerical investigation of fiber transmission of a chaotic encrypted message using dispersion compensation schemes,” J. of Lightwave Technol. **22**,2256–2263 (2004). [CrossRef]

_{2}= 0.1 ps

^{2}/km, β

_{3}= 0.1 ps

^{3}/km, and γ = 1.5 W

^{-1}km

^{-1}, respectively.

^{2}=

*n*(

_{sp}hf*G*- 1)Δ

*f*, where

*G*is the amplifier gain to compensate transmission loss,

*n*accounts for incomplete population inversion,

_{sp}*h*is Plank’s constant,

*f*is the signal carrier frequency and Δ

*f*is the bandwidth occupied by each discrete Fourier spectrum component. In our simulation,

*n*is set to 2, or noise figure of 6 equivalently.

_{sp}### 3.2. Results with fiber transmission module

^{-9}(dashed line), the benchmark set by conventional communications, can be achieved for fiber shorter than 150 km with a 1 Gbps message bit-rate. For higher message bit-rate, the performance of the OOSK scheme is severely degraded compared to the ACM scheme. Fig. 4(b) shows the BER of the ACM and the OOSK schemes with different message bit-rates. As can be seen, while both schemes deteriorate as the bit-rate increases, the ACM scheme clearly outperforms the OOSK scheme except in the case of very low bit-rate. This is because that, in the OOSK scheme, the message is encoded by switching the laser back and forth between two different chaotic states. As the message bit-rate increases and approaches the relaxation oscillation frequency of the laser, the laser does not have sufficient time to stabilize in one state before it is suddenly being switched to the other. Hence, this transient effect makes message recovery more difficult that large synchronization errors are observed in both the ON and the OFF states. Compared to the OOSK scheme, message modulation in the ACM scheme is done within the same chaotic state. Therefore, since the transmitter and the receiver lasers are synchronized at all time, it shows comparable better message recovery quality. Nevertheless, the maximum achievable bit-rate for both schemes are ultimately limited by the relaxation oscillation frequency of the laser (in our case

*f*= 2.5 GHz).

_{r}*γ*and

_{c}*γ*, but not as much in the mismatch in

_{n}*γ*and

_{s}*γ*. For the OOSK scheme, the performance with negative parameter mismatch is fairly robust while it drops sharply with positive mismatch. Since the transmitter laser is switched between two different chaotic attractors, the performance (or equivalently, the shape of the curve) of the OOSK scheme is strongly depending on the attractors of the ON and OFF states initially chosen. In any case, the performances of both schemes are shown to be at a level above the benchmark (Q= 6)in a range of mismatch of around 10 percents, which is considered practical in real applications. More detailed analysis on the robustness of this chaotic communication system will be reported separately.

_{p}## 4. Radio-over-fiber transmission

### 4.1. Description of the wireless channel

20. L. Wei and C. Schlegel, ”Synchronization requirements for multi-user OFDM on satellitemobile and two-path Rayleigh fading channels,” IEEE Trans. on Commun. **43**,887–895 (1995). [CrossRef]

*s*and the probability density function

_{r}*p*(

*r*) of Rayleigh channel can be expressed by

*r*exp(

*jθ*) = ∑

^{n}

_{i=1}

*a*exp(

_{i}*jθ*), ω

_{i}_{0}is the angular frequency of signal,

*n*is the total number of the signals,

*a*and

_{i}*θ*present the amplitude and the phase of the

_{i}*i*path, and σ

_{th}^{2}

_{r}is the Gaussian random variables, respectively. An indoor environment of the wireless channel is assumed that the path delay and attenuation are randomly distributed between 1 to 100 ns and 0 to -20 dB, respectively.

### 4.2. Results with wireless channel

^{-10}while the ACM scheme has a BER worse than 10

^{-7}. This is because the decoding in the ACM scheme requires precise synchronization to recover the encoded message and which becomes very difficult when elevated noise and random effects are presented. On the contrary, it is comparably easy in the OOSK scheme that the decoding is done simply by distinguishing if the transmitter and the receiver lasers are in the same or different states. Figures 8(a) and (b) show the performance of the ACM and the OOSK schemes for different SNR without and with the multipath effect, respectively. As can be seen in Fig. 8(a), while both schemes can achieve a benchmark performance of BER= 10

^{-9}, the OOSK scheme performs slightly better than the ACM scheme when only the path loss and AWGN noise are included in the wireless channel. When the multipath effect is taken into account, as shown in Fig. 8(b), the OOSK scheme clearly outperforms the ACM scheme and the benchmark can still be reached for SNR above 35 dB. As the result, the OOSK schemes shows to possess better noise tolerability than the ACM scheme, which is extremely important in a practical communication environment such as the ROF scenario discussed here.

## 5. Conclusion

## References and links

1. | F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. |

2. | S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun. |

3. | T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling route to chaos in a semiconductor laser subject to optical injection,” Appl. Phys. Lett. |

4. | T. Mukai and K. Otsuka, “New route to optical chaos: successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. |

5. | J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. |

6. | F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. |

7. | S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. |

8. | F. Y. Lin and J. M. Liu, “Harmonic frequency locking in a semiconductor laser with delayed negative optoelectronic feedback,” Appl. Phys. Lett. |

9. | N. Gastaud, S. Poinsot, L. Larger, J. M. Merolla, M. Hanna, J. P. Goedgebuer, and F. Malassenet, ”Electro-optical chaos for multi-10 Gbit/s optical transmissions” Electron. Lett. |

10. | J. M. Liu, H. F. Chen, and S. Tang, ”Synchronized chaotic optical communications at high bit rates,” IEEE J. Quantum Electron. |

11. | J. Ohtsubo, ”Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. |

12. | Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, ”Communication using synchronization of optical-feedback-induced chaos in semiconductor lasers,” IEEE Trans. Circuits Syst. I |

13. | D. Kanakidis, A. Argyris, and D. Syvridis, ”Performance characterization of high-bit-rate optical chaotic communication systems in a back-to-back configuration,” J. of Lightwave Technol. |

14. | A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, ”Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature |

15. | D. Kanakidis, A. Bogris, A. Argyris, and D. Syvridis, ”Numerical investigation of fiber transmission of a chaotic encrypted message using dispersion compensation schemes,” J. of Lightwave Technol. |

16. | S. Tang and J. M. Liu, ”Chaos synchronization in semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. |

17. | H. D. I. Abarbanel, M. B. Kennel, L. Illing, S. Tang, H. F. Chen, and J. M. Liu, ”Synchronization and communication using semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. |

18. | J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron. |

19. | V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, ”Optimization of the split-step Fourier method in modeling optical-fiber communication systems,” J. Lightwave Technol. |

20. | L. Wei and C. Schlegel, ”Synchronization requirements for multi-user OFDM on satellitemobile and two-path Rayleigh fading channels,” IEEE Trans. on Commun. |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(140.5960) Lasers and laser optics : Semiconductor lasers

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: October 20, 2006

Revised Manuscript: December 20, 2006

Manuscript Accepted: January 10, 2007

Published: January 22, 2007

**Citation**

Fan-Yi Lin and Meng-Chiao Tsai, "Chaotic communication in radio-over-fiber transmission based on optoelectronic feedback semiconductor lasers," Opt. Express **15**, 302-311 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-2-302

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### References

- F. Y. Lin and J. M. Liu, "Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback," Opt. Commun. 221,173-180 (2003). [CrossRef]
- S. K. Hwang and J. M. Liu, "Dynamical characteristics of an optically injected semiconductor laser," Opt. Commun. 183,173-180 (2003).
- T. B. Simpson and J. M. Liu, A. Gavrielides, V. Kovanis, P. M. Alsing, "Period-doubling route to chaos in a semiconductor laser subject to optical injection," Appl. Phys. Lett. 64,3539-3541 (1994). [CrossRef]
- T. Mukai and K. Otsuka, "New route to optical chaos: successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity," Phys. Rev. Lett. 55,1711-1714 (1985). [CrossRef] [PubMed]
- J. Mork, B. Tromborg, and J. Mark, "Chaos in semiconductor lasers with optical feedback: theory and experiment," IEEE J. Quantum Electron. 28, 93-108 (1992). [CrossRef]
- F. Y. Lin and J. M. Liu, "Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback," IEEE J. Quantum Electron. 39,562-568 (2003). [CrossRef]
- S. Tang and J. M. Liu, "Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback," IEEE J. Quantum Electron. 37,329-336 (2001). [CrossRef]
- F. Y. Lin and J. M. Liu, "Harmonic frequency locking in a semiconductor laser with delayed negative optoelectronic feedback," Appl. Phys. Lett. 81,3128-3120 (2002). [CrossRef]
- N. Gastaud, S. Poinsot, L. Larger, J. M. Merolla, M. Hanna, J. P. Goedgebuer and F. Malassenet, "Electro-optical chaos for multi-10 Gbit/s optical transmissions" Electron. Lett. 40, (2004). [CrossRef]
- J. M. Liu, H. F. Chen, and S. Tang, "Synchronized chaotic optical communications at high bit rates," IEEE J. Quantum Electron. 38,1184-1196 (2002). [CrossRef]
- J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron. 38,1141-1154 (2002). [CrossRef]
- Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, "Communication using synchronization of optical-feedbackinduced chaos in semiconductor lasers," IEEE Trans. Circuits Syst. I 48,1484-1490 (2001). [CrossRef]
- D. Kanakidis, A. Argyris, and D. Syvridis, "Performance characterization of high-bit-rate optical chaotic communication systems in a back-to-back configuration," J. of Lightwave Technol. 21,750-758 (2003). [CrossRef]
- A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature 438,343-346 (2005). [CrossRef] [PubMed]
- D. Kanakidis, A. Bogris, A. Argyris, and D. Syvridis, "Numerical investigation of fiber transmission of a chaotic encrypted message using dispersion compensation schemes," J. of Lightwave Technol. 22,2256-2263 (2004). [CrossRef]
- S. Tang and J. M. Liu, "Chaos synchronization in semiconductor lasers with optoelectronic feedback," IEEE J. Quantum Electron. 39,708-715 (2003). [CrossRef]
- H. D. I. Abarbanel, M. B. Kennel, L. Illing, S. Tang, H. F. Chen, and J. M. Liu, "Synchronization and communication using semiconductor lasers with optoelectronic feedback," IEEE J. Quantum Electron. 37,1301-1311 (2001). [CrossRef]
- J. M. Liu and T. B. Simpson, "Four-wave mixing and optical modulation in a semiconductor laser," IEEE J. Quantum Electron. 30,957-965 (1994). [CrossRef]
- V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communication systems," J. Lightwave Technol. 21,61-68 (2003). [CrossRef]
- L. Wei and C. Schlegel, "Synchronization requirements for multi-user OFDM on satellitemobile and two-path Rayleigh fading channels," IEEE Trans. on Commun. 43,887-895 (1995). [CrossRef]

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